## anonymous 3 years ago I don't really get this. Question: Use the rules for exponents and roots to prove that 512^2/3 = 16^3/2

1. anonymous

Do you mean a rigorous formal proof?

2. anonymous

I don't really know. This is what the question was and I don't get it.

3. anonymous

Do you understand how to use logarithms?

4. anonymous

No

5. anonymous

Ah, you will want to understand natural logarithms for this question, I can explain it.

6. anonymous

$y = \log_b x$ $x = b^y$

7. anonymous

If we take the natural logarithm of $512^{\frac{2}{3}}$ $\frac{2}{3}\ln(512)$

8. anonymous

We can pull the exponent out

9. anonymous

So, is that a cube root? That we ended up with?

10. precal

|dw:1360950294527:dw|

11. precal

|dw:1360950347726:dw|

12. precal

|dw:1360950360574:dw|

13. precal

|dw:1360950390774:dw|

14. precal

|dw:1360950432326:dw|

15. precal

yes they are both equivalent

16. anonymous

Thanks, so much. That makes sense now.

17. precal

yw

18. precal

no need to use logs here

19. anonymous

just using exponents :512=2^9 so 512^(2/3)=2^6 and 16^(3/2)=2^6 so both are equal

20. anonymous

Thanks

21. precal

yw